Self-rotation-symmetry transformation for tuning anisotropy of single type lattice structures with minimal surfaces

There have been many works on the mechanical properties of hybrid structures based on triply periodic minimal surfaces (TPMSs) with multiple types. However, hybrid structures with a single type are neglected, which casts a shadow over searching the properties of a single structural element. Here we propose a self-rotation-symmetry transformation (SRST) method to numerically and experimentally show that isotropy and anisotropy can be realized on one TPMS type. With SRST, multiple substructures with the same type rotate with angle θ and then symmetrically combine to form a new unit. With the change of θ , the ratio maximum to minimum modulus (Max/Min) of the 2D SRST P type unit is from 1.02 to 2.03, and that of the 3D SRST P type unit is from 1.07 to 2.15. Also, the SRST method can effectively tune elastic modulus in a given direction. For example, the elastic modulus is tuned from about 200–300 MPa for the 2D P lattice. Interestingly, the elastic modulus and anisotropy are changed independently of the volume fraction, since the volume of each substructure does not change when rotated. This method provides the feasibility of designing targeted mechanical properties with a targeted volume fraction for applications in energy, aerospace, optics, and medical fields.